A local adaptive mesh refinement algorithm for solving hyperbolic systems of conservation laws in three space dimensions is described. The method is based on the use of local grid patches superimposed on a coarse grid to achieve sufficient resolution in the solution. A numerical example computing the interaction of a shock with a dense cloud in a supersonic inviscid regime is presented. Detailed timings are given to illustrate the performance of the method in three dimensions.
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Bell et al. (1994) studied this question.
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